State Standards: GLEs/GSEs National Content Standards:
Grade Span Expectations [Math]: M(N&O)–10–8 Applies properties of numbers to solve problems, to simplify computations, or to compare and contrast the properties of numbers and number systems.
M(F&A)–10–1 Identifies, extends, and generalizes a variety of patterns (linear and nonlinear) represented by models, tables, sequences, or graphs to solve problems.
M(PRP)–HS–1 Students will use problem-solving strategies to investigate and understand increasingly complex mathematical content and be able to: • Expand the repertoire of problem-solving strategies and use those strategies in more sophisticated ways. • Use technology whenever appropriate to solve real-world problems (e.g., personal finance, wages, banking and credit, home improvement problems, measurement, taxes, business situations, purchasing, and transportation). • Formulate and redefine problem situations as needed to arrive at appropriate conclusions.
Grade Span Expectations [Physics]:
PS3 (7-8) 8: Students demonstrate and understanding of motion by… (8a)… measuring the distance and time for a given moving object and using those values to calculate speed. (8b)… Solving for any unknown in the expression v=d/t given values for the other two variables. (8c)… Differentiating between speed, velocity and acceleration.
PS3 (9-11) 8: Students demonstrate and understanding of forces and motion by… (8a)… Predicting and/or graphing the path of an object in different reference planes and explain how and why it occurs. (8b)… Using modeling, illustrating, and graphing to explain how distance and velocity change over time for a free falling object.
PS3 (Ext) 8: Students demonstrate an understanding of forces and motion by… (8aa)… Using a quantitative representation of how distance and velocity change over time for a free falling object. (8bb)… Using a quantitative representation of the path of an object that has both horizontal and free fall motion. (8cc)… Modeling, illustrating, graphing, and or quantitatively explaining the path of an object that has both horizontal and free fall motion.
Context of the Lesson Where does this lesson fit in the curriculum and instructional context? Is it the opening of a unit or a series of lessons?
This lesson is designed to be the final lesson of the projectile motion unit for Physics 1 or Physics 1 (H) classes. Prior to this lesson the students will have been introduced to 2 dimensional kinematics problems and will have had extensive practice working with a variety of different types of problems. They will understand how to apply the problem solving steps in order to solve a problem and they will be proficient with breaking vectors into components.
It will be necessary that students have a strong mathematical background for this particular lesson. They should be proficient in manipulating equations that involve 1 unknown and they should also know how to solve simultaneous equations involving two unknowns.
With this prerequisite knowledge the students will be prepared for this lesson and will be successful.
This lesson provides the students with further practice working with the kinematics equations and with applying the physical concepts to the real world and to their own lives.
Opportunities to Learn
Differentiation: Materials, Learners and Environments
Plans to differentiate instruction:
This lesson is split up into two different segments. This first segment involves the students working in groups to develop kinematics problems. They will form a multi part problem involving kinematics/ projectile motion situations. The second portion involves the students swapping problems with the other groups and attempting to solve the problems that their peers developed.
These two segments require different levels of thought and will be beneficial for different types of learners. Kinesthetic and visual learners will enjoy making diagrams for the problems that they develop while students who enjoy real world applications will like creating different scenarios within the problems. Traditional learners will find the segment beneficial where they will be asked to solve their classmate’s problems. Students who enjoy working collaboratively will also find this activity beneficial.
For the students that may find this task too easy I can issue them the challenge of trying to “stump” one of their fellow classmates who is also advanced. This will create a small competition that the advanced students may find entertaining to participate in. For the students that may be struggling I will provide assistance for them and will help to walk them through the problem solving steps to solve the problems that their classmates developed. Accommodations and modifications: Environment factors: This lesson involves two separate activities. The first activity will be performed in groups and these groups will gather together at the lab benches that are located around the room. I will try to position some of the groups near the whiteboards so that they can outline their thoughts and ideas on the whiteboard. The second activity will be performed in the same groups and the students will simply swap problems. Materials: ü Small whiteboards
Objectives
Students will demonstrate their understanding of projectile motion by successfully developing questions/problems for their classmates and successfully solving their classmates’ problems.
Instructional Procedures
LAUNCH A: At the start of this lesson, as the students walk into the classroom, I will instruct them all the work on the problem that I have posted on the whiteboard. This problem will have been taken from a previous NECAP exam and will be in the NECAP format. This will give the students experience with these types of problems and the way in which test questions will be formulated. Once everyone has arrived at class and has worked on the question on the whiteboard we will discuss the answer as a class and I will ask for a volunteer who would like to explain how they went about solving the problem. I will then explain to the students what they will be doing during that period. “We have spent a lot of class time lately solving problems that I have created for you. You’ve seen many different types of problems involving objects with horizontal and free fall motion simultaneously. Today it’s your turn to make the problems! I’m going to place you in groups of 4 and your job is to create a problem for your classmates to solve” “If your group is able to develop a problem that the other groups cannot solve then you will receive 2 EC pts toward the assessment that we will have next week” The students will form their own groups and they will work to try to develop a difficult problem for their peers to solve. I will allow them to choose their own groups for the first part of the lesson. During this activity I will walk around the room and I will check over the problems that the students have developed. If they think they have formed their final version I will check it over to make sure that it is indeed solvable and that the answer that they have found is the correct one. I may also offer some guiding questions to the students to help them develop more parts to their problems and make their questions slightly more challenging. “Is it necessary to give that much information within the problem? What is the least amount of information that can be given?” “If you embed this situation into a word problem some students will find it more challenging!” “If you calculate distance you can also ask them to find the total time” “Can you develop a problem that relates to your own lives?” For students that may be struggling with this task I will help them come up with a situation to develop their questions around. I will ask them about their hobbies and try to think of ways to incorporate those into the development of a physics problem. “Can you develop a problem that relates to your own lives?” EXPLORE A: After all of the groups have finished developing their questions they will have to make a final version in which they neatly write their question on a blank white piece of paper. Each group will have a number designated to them and they will have to write this number on the top of their problem. The students will then pass their problem to the next group in a clockwise fashion. The groups will work on the other groups’ problems and record their results in their notebooks on separate sheets of paper ( a new sheet for each new problem). If they are stuck they can ask the original group for assistance/ hints. Once a group finished with one problem they can trade with another group that has also finished. Ideally every group should be able to attempt to complete every other group’s problem. SUMMARIZE/SHARE A: Once all of the groups have finished working on the other group’s problems they will pass their answers to the creators of the problems. The creators can then grade the work of their classmates and see if they were able to stump any of the other groups. The group that stumped the greatest number of other groups will receive 2 EC points towards their final assessment. Each group will then have to go to the front of the classroom and explain to the class how they intended for everyone to solve their problem. They will walk through the problem solving steps and show how it can be solved. This will serve as a great review for the students because they will be having an assessment the following week.
Assessment
In order to assess my students during this investigation I will determine whether each student has successfully completed each of the objectives described above. Launch A: During the first portion of this activity I will assess my students on their ability to work cooperatively in groups. I will informally assess them on how well they are able to apply their knowledge of kinematics and of projectile motion to develop an original challenging problem for their peers. I will be able to observe their critical thinking skills as well as their ability to use higher levels of thinking. I will take notes during this session as part of the informal assessment. Explore/Summarize A: During the second portion of this lesson I will also informally assess the students. This time I will assess them on their ability to use the problem solving steps to solve their classmates’ problems. I will also informally assess them as they present their problem to the class at the end of the instructional period.
Reflections This section to be completed only if lesson plan is implemented.
Lesson Implementation: Was not able to implement this lesson yet.
Lesson #9: It’s Your Turn! A Student Challenge
Lesson Title
It’s Your Turn! A Student Challenge
National Content Standards:
M(N&O)–10–8 Applies properties of numbers to solve problems, to simplify computations, or to compare and contrast the properties of numbers and number systems.
M(F&A)–10–1 Identifies, extends, and generalizes a variety of patterns (linear and nonlinear) represented by models, tables, sequences, or graphs to solve problems.
M(PRP)–HS–1 Students will use problem-solving strategies to investigate and understand increasingly complex mathematical content and be able to:
• Expand the repertoire of problem-solving strategies and use those strategies in more sophisticated ways.
• Use technology whenever appropriate to solve real-world problems (e.g., personal finance, wages, banking and credit, home improvement problems, measurement, taxes, business situations, purchasing, and transportation).
• Formulate and redefine problem situations as needed to arrive at appropriate conclusions.
Grade Span Expectations [Physics]:
PS3 (7-8) 8: Students demonstrate and understanding of motion by…
(8a)… measuring the distance and time for a given moving object and using those values to calculate speed.
(8b)… Solving for any unknown in the expression v=d/t given values for the other two variables.
(8c)… Differentiating between speed, velocity and acceleration.
PS3 (9-11) 8: Students demonstrate and understanding of forces and motion by…
(8a)… Predicting and/or graphing the path of an object in different reference planes and explain how and why it occurs.
(8b)… Using modeling, illustrating, and graphing to explain how distance and velocity change over time for a free falling object.
PS3 (Ext) 8: Students demonstrate an understanding of forces and motion by…
(8aa)… Using a quantitative representation of how distance and velocity change over time for a free falling object.
(8bb)… Using a quantitative representation of the path of an object that has both horizontal and free fall motion.
(8cc)… Modeling, illustrating, graphing, and or quantitatively explaining the path of an object that has both horizontal and free fall motion.
Where does this lesson fit in the curriculum and instructional context? Is it the opening of a unit or a series of lessons?
It will be necessary that students have a strong mathematical background for this particular lesson. They should be proficient in manipulating equations that involve 1 unknown and they should also know how to solve simultaneous equations involving two unknowns.
With this prerequisite knowledge the students will be prepared for this lesson and will be successful.
This lesson provides the students with further practice working with the kinematics equations and with applying the physical concepts to the real world and to their own lives.
Differentiation: Materials, Learners and Environments
This lesson is split up into two different segments. This first segment involves the students working in groups to develop kinematics problems. They will form a multi part problem involving kinematics/ projectile motion situations. The second portion involves the students swapping problems with the other groups and attempting to solve the problems that their peers developed.
These two segments require different levels of thought and will be beneficial for different types of learners. Kinesthetic and visual learners will enjoy making diagrams for the problems that they develop while students who enjoy real world applications will like creating different scenarios within the problems. Traditional learners will find the segment beneficial where they will be asked to solve their classmate’s problems. Students who enjoy working collaboratively will also find this activity beneficial.
For the students that may find this task too easy I can issue them the challenge of trying to “stump” one of their fellow classmates who is also advanced. This will create a small competition that the advanced students may find entertaining to participate in.
For the students that may be struggling I will provide assistance for them and will help to walk them through the problem solving steps to solve the problems that their classmates developed.
Accommodations and modifications:
Environment factors:
This lesson involves two separate activities. The first activity will be performed in groups and these groups will gather together at the lab benches that are located around the room. I will try to position some of the groups near the whiteboards so that they can outline their thoughts and ideas on the whiteboard. The second activity will be performed in the same groups and the students will simply swap problems.
Materials:
ü Small whiteboards
Instructional Procedures
At the start of this lesson, as the students walk into the classroom, I will instruct them all the work on the problem that I have posted on the whiteboard. This problem will have been taken from a previous NECAP exam and will be in the NECAP format. This will give the students experience with these types of problems and the way in which test questions will be formulated. Once everyone has arrived at class and has worked on the question on the whiteboard we will discuss the answer as a class and I will ask for a volunteer who would like to explain how they went about solving the problem.
I will then explain to the students what they will be doing during that period.
“We have spent a lot of class time lately solving problems that I have created for you. You’ve seen many different types of problems involving objects with horizontal and free fall motion simultaneously. Today it’s your turn to make the problems! I’m going to place you in groups of 4 and your job is to create a problem for your classmates to solve”
“If your group is able to develop a problem that the other groups cannot solve then you will receive 2 EC pts toward the assessment that we will have next week”
The students will form their own groups and they will work to try to develop a difficult problem for their peers to solve. I will allow them to choose their own groups for the first part of the lesson. During this activity I will walk around the room and I will check over the problems that the students have developed. If they think they have formed their final version I will check it over to make sure that it is indeed solvable and that the answer that they have found is the correct one. I may also offer some guiding questions to the students to help them develop more parts to their problems and make their questions slightly more challenging.
“Is it necessary to give that much information within the problem? What is the least amount of information that can be given?”
“If you embed this situation into a word problem some students will find it more challenging!”
“If you calculate distance you can also ask them to find the total time”
“Can you develop a problem that relates to your own lives?”
For students that may be struggling with this task I will help them come up with a situation to develop their questions around. I will ask them about their hobbies and try to think of ways to incorporate those into the development of a physics problem.
“Can you develop a problem that relates to your own lives?”
EXPLORE A:
After all of the groups have finished developing their questions they will have to make a final version in which they neatly write their question on a blank white piece of paper. Each group will have a number designated to them and they will have to write this number on the top of their problem. The students will then pass their problem to the next group in a clockwise fashion.
The groups will work on the other groups’ problems and record their results in their notebooks on separate sheets of paper ( a new sheet for each new problem). If they are stuck they can ask the original group for assistance/ hints. Once a group finished with one problem they can trade with another group that has also finished.
Ideally every group should be able to attempt to complete every other group’s problem.
SUMMARIZE/SHARE A:
Once all of the groups have finished working on the other group’s problems they will pass their answers to the creators of the problems. The creators can then grade the work of their classmates and see if they were able to stump any of the other groups. The group that stumped the greatest number of other groups will receive 2 EC points towards their final assessment.
Each group will then have to go to the front of the classroom and explain to the class how they intended for everyone to solve their problem. They will walk through the problem solving steps and show how it can be solved. This will serve as a great review for the students because they will be having an assessment the following week.
Launch A:
During the first portion of this activity I will assess my students on their ability to work cooperatively in groups. I will informally assess them on how well they are able to apply their knowledge of kinematics and of projectile motion to develop an original challenging problem for their peers. I will be able to observe their critical thinking skills as well as their ability to use higher levels of thinking. I will take notes during this session as part of the informal assessment.
Explore/Summarize A:
During the second portion of this lesson I will also informally assess the students. This time I will assess them on their ability to use the problem solving steps to solve their classmates’ problems. I will also informally assess them as they present their problem to the class at the end of the instructional period.
This section to be completed only if lesson plan is implemented.